Role of ventilation on the transmission of viruses in buildings, from a single zone to a multizone approach

Abstract In a virus pandemic context, buildings ventilation has been recognized as a solution for preventing transmission of the virus in aerosolized form. The impact of the widespread recommendation of window opening and sealing door on ventilation circuits needs to be considered with a multizone approach. We modeled the airflow distribution in a building where people are isolating in a pandemic context, including one infected person. We analyzed the impact of opening the window and sealing the door in the quarantine room on exposures and probability of infection for occupants of the flat and of adjacent flats. In order to study the sensitivity of the results, we tested three ventilation systems: balanced, exhaust‐only, and humidity‐based demand‐controlled, and several window‐ and door‐opening strategies. When the door of the quarantine room is sealed, we observe that opening the window in the quarantine room always results in increased exposure and probability of infection for at least one other occupant, including in neighbors' apartments. When all internal doors are opened, we observe moderate impacts, with rather an increase of exposure of the occupants of the same apartments and of their probability of infection, and a decrease for the occupants located in other apartments. Based on the analysis on the airflows distribution in this case study, we conclude that sealing the internal door has more influence than opening the window of the quarantine room, whatever the ventilation system. We observe that this widespread recommendation to open the window of a quarantine room and to seal the door is based on the consideration of a single zone model. We illustrate the importance of moving from such a single zone approach to a multizone approach for quantifying ventilation and airing impacts in multizone buildings as residences in order to prevent epidemics of viruses such as SARS‐CoV‐2. It highlights the need of air leakage databases.


| Aerosol transmission of viruses including SARS-CoV-2
During previous pandemics created by influenza-type viruses (influenza, avian influenza) and corona viruses (SARS-CoV-1, MERS), the predominant modes of transmission were via drops, droplets, and contact with contaminated surfaces. However, evidence highlighted the risk of formation of aerosols that could travel through the air, originating from either the sneezing or the feces, depending on the environmental conditions that allow (or prevent) the survival and travel capability of the infectious aerosols. [1][2][3][4][5] When we breathe, speak, sing, cough, and sneeze, droplets of all sizes are emitted and moved by a turbulent, hot, and humid (breathing) cloud of gas. It keeps them at a high concentration level over several meters where it transports them in a few seconds. Then, when the cloud slows down sufficiently, ventilation, specific airflow patterns become important, viral load of the emitter, duration of exposure, and susceptibility of an individual to infection are also important, as well. 3 Using high-frequency imaging measurements on volunteers, it has been shown that when individuals coughed and/or sneezed, in addition to the projecting drops and droplets an aerosol was formed, which could travel over distances of 6-8 m. 6,7 Aerosol transmission of SARS-CoV-2 was underestimated at the beginning of the pandemic. Today, several articles demonstrate that this is an important, and even the dominant, mode of transmission. 4,8,9 The first experimental study by van Doremalen et al. 10 attempts to reproduce, by nebulization, the airborne suspension of the virus after a patient had coughed. These researchers showed that SARS-CoV-2 could survive for 3 h as an aerosol (<5 μm).
Several case studies and scientific articles continued this line of investigation and highlighted the risk of airborne transmission of the SARS-CoV-2. [11][12][13][14][15][16][17] Several scientists acted to alert both the international scientific community and public decision-makers. They call for aerosol transmission of the SARS-CoV-2 to be taken into account for more effective prevention of evolutions in the epidemic. [18][19][20][21][22][23] They reiterate the importance of taking into account more recent and accurate models of aerosol formation, phase change, and transport, which clearly call into question the current recommendations on the social distance to be maintained between people, that is, 1 to 2 m, at least indoor. 3,4 Even if various issues still need to be resolved, 24 this way of transmission has been recognized by WHO 25

and the American and
European centers for disease prevention and control CDC, 26,27 and several countries implemented airing in the list of barrier gestures or actions on building ventilation systems, or in national protocols, in order to prevent the COVID-19 transmission. 26,28-30

| Key role of ventilation in buildings: energy, IAQ, and virus transmission
Ventilation and airflows in buildings constitute an important research area regarding their crucial impacts on two issues: indoor air quality and reducing heating energy consumption.
Indeed, on the contrary, since people spend 60%-90% of their life indoors (in dwellings, offices, and schools), indoor air quality (IAQ) is a major factor affecting public health. [31][32][33][34][35] On the contrary, indoor environments can often be more polluted than outdoor ones. 36 As a result, according to the World Health Organization, 37 99 000 deaths in Europe were attributable to indoor air pollution in 2012. Some authors showed that due to heavier occupation of dwellings during the COVID-19 lockdown, coupled with changes in activities (more cooking, more cleaning) and a lack of ventilation adaptation options, indoor air pollutants could reach levels hazardous to occupants' health. 38 They advise taking measures to address this if further stay-at-home orders are issued in future epidemic-related lockdowns.
The building energy performance perspective requires efforts to rethink ventilation airflows because of their impact on thermal losses. In this context, more attention is given to the ventilation design and on-site implementation, [39][40][41][42][43] and ventilation systems are becoming more energy efficient with balanced systems including heat recovery or smart systems with variable airflows. [44][45][46] The current COVID-19 epidemic has highlighted another building ventilation issue: prevention of disease spread. The literature review analyzing air-transported viruses points out a lack of data to push work forward from theory to prevention practices, particularly regarding which ventilation conditions have a strong impact on the environmental contexts that favor (or hamper) the survival

Practical Implications
• In an aerosolized virus pandemic context, airflow distribution in buildings is a crucial issue.
• Thus, it is important to precisely assess the airflows in the building with multizone modeling considering air leakage distributions to prevent from the virus dissemination.
• Prevention actions should secure that airflows circulate from low-contaminated zones to high-contaminated zones.
• The multizone modeling approach shows that opening a window and sealing the door in a high-infected room, as a quarantine room, may cause a risk for other noncontaminated occupants of the building. and transport of infectious aerosols. 5  • The need to restart ventilation at least 2 h before occupancy.
• General advice is to provide as much fresh outdoor air as is reasonably possible. The key aspect is the amount of fresh air provided per person.
• To actively use openable windows (much more than normal, even when this causes some thermal discomfort). Window opening is then the only way to boost air exchange rates. Windows should be opened for approximately 15 min when entering the room (especially when the room was occupied by others beforehand).
Also, in buildings with mechanical ventilation, window opening can be used to boost ventilation further.
• Open toilet windows should be avoided to maintain negative pressure in the toilets and the right direction of mechanical ventilation.
In contrast to REHVA, ASHRAE does not recommend maximum airing but rather the minimum necessary, they warn of the risk of creating thermal discomfort which would reduce the resistance of individuals to infection. Furthermore, airing to the maximum creates energy, comfort, and indoor air quality issues. 52,53 With the exception of the last measure proposed by the REHVA (avoid opening windows in toilets), published literature and technical guidelines on ventilation rarely take into account the risk of contamination within zones of the same building. However, a few rarer published examples also demonstrate the possibility of transmission of the virus between different rooms in a building. New Zealand had set up dedicated isolation hotels where all people wishing to enter the country had to stay. Each person was regularly tested, and studies showed that aerosol contamination between rooms in this hotel was very likely. 54 In another cluster, neighbors who had no direct contact with each other became infected in an apartment building in Seoul. 55 To summarize, several practical recommendations on ventilation in a virus pandemic context have been published for some types of building and are very useful in the field. Nevertheless, we observe that ventilation is mainly considered from a single-zone point of view, and not from a multizone point-of-view. Therefore, it is considered that the higher the air change rate (through ventilation and/ or airing), the lower the risk of infection. However, we should make sure that the higher the air change rate in an area, the lower the risk of infection in that area, but also in all connected areas, which is far from obvious. We propose to address this research gap through a multi-zone modeling approach.

| Research issue
The novelty of this research is to better understand the interaction between airflows passing through windows, through leakage points, and through the ventilation components in multizone buildings and how they impact the effectiveness of prevention strategies, as the opening of windows and doors in a context such as the SARS-CoV-2 pandemic.
Multizone approach is crucial as the literature shows how CO 2 and pollutant concentrations can strongly vary from a room to another one in residential buildings. 56 propose to use as a metric the absolute average fractional differences-D AAF , defined as the difference between two concentration values (one in a room, one in another room) divided by the average of the two. It can reach 48% for VOC, 56,57 80% for CO 2 58 to 171% 59 for CO 2 , between the living room and one bedroom or between two bedrooms. Based on CO 2 measurements in ten homes 60 showed that only 60% of the homes could be considered uniform. In many buildings of Western Europe, as residences, schools, and office workplaces. whole-house ventilation is often designed using a multizone approach, with airflows circulating between rooms. [67][68][69][70][71] Such ventilation systems are categorized in three categories: balanced ventilation, exhaust-only ventilation, and supply-only ventilation. They all work on the same principle: ventilate from the less polluted zones, to the most polluted ones, generally the humid rooms: toilets, bathrooms, and kitchens.
Theoretically, exhaust-only mechanical ventilation in dwellings works on the principle of inlets drawing outdoor air into bedrooms and living rooms, and outlets exhausting air from rooms with high moisture levels ( Figure 1A). Nevertheless, high air leakage on exterior walls of the higher-humidity rooms could bypass the bedrooms, leading them to become under-ventilated (bedrooms in Figure 1B). Opening windows amplifies this disturbance of the theoretical aeraulic circuits.
The pandemic context raises two crucial issues: • Firstly, what is the impact of moving from a design based on air flows from the least polluted areas (bedrooms, living rooms, offices, and classrooms) to the most polluted areas (bathrooms, toilets, and kitchen), if a normally low-pollution area becomes a high-pollution area (e.g., a bedroom becoming a quarantine room)?
• Secondly, what is the impact of the widespread recommendation to open windows on ventilation systems, and more generally on the infection risk of occupants?
In order to answer these two questions, we model in this study the airflow distribution due to the opening of windows in a multifamily building, where a sick person is isolated in a pandemic context such as COVID-19. The transport of an aerosolized virus is simplified by modeling the movement of contaminated particles.
We will focus on the airflows between rooms in dwellings with high concentrations of viral particles, which will allow us to assess the exposure of occupants to the contaminated aerosol and the risk of infection.
To investigate the sensitivity of the results, we test three ventilation systems, a balanced constant airflow system, a constant airflow system with exhaust only, a humidity-controlled demand system, and several strategies for opening windows and doors to maximize the air change rate in the rooms.

| Presentation of the case study
The case study is a real multi-family building with houses rental accommodation, spread over eight floors. We are particularly in- The modeling of the staircase is highly simplified. It is modeled as a transfer zone, unventilated, heated, with no leakage to the outside.
Indeed, we focus in this approach on direct transfer between flats, and therefore underestimate the risk of transmission.
Overall air leakage from the envelope has been measured applying the ISO 9972 procedure; and is n 50 = 1.5 h −1 .
We assume that two inhabitants live in the master bedroom  Table 2. We focus our analysis on the most exposed occupants, in bold in this table.

| Multizone approach
We investigate airflows and particle concentrations using numerical modeling with CONTAM software. [72][73][74] The validation of such multizone models is well documented and has been compared with experimental results. [74][75][76][77][78][79] Several authors have shown that this type of model, assuming well-mixed air in every zone, is a good fit for ventilation and IAQ modeling. 80,81 Each room in the house is modeled as one air zone (making a total of 11 zones). The indoor temperature is assumed to be maintained at 20°C during this period, by means of the heating system. 82 The air mass balance equation is considered for each zone as follows: Where q i,j are the mass airflows entering or leaving zone i through leaks, door undercuts, and passive components (trickle vents/grilles on external walls) from all the adjacent zones j (and outside), q V,I is the airflow extracted or supplied by the mechanical ventilation system in zone i.
Airflow rate through leaks is calculated from the pressures and the leakage characteristics, using the power law (Equation 2).
Where i is the air density in the origin zone i [kg m −3 ], C i,j the air leak-

| Weather data
We use typical dynamic meteorological data for two winter weeks

| Air leakage distribution
In practice, leaks are everywhere in buildings (around windows, electric components, and cracks). 83 In order to simplify this complex distribution, we modeled air leakage in CONTAM by one path at the center of each external and internal partition wall in each zone, using the power law (Equation 2).
For the external walls of the multi-family building, we use data from on-site measurements as the permeability of each dwelling was measured. For the apartments R,D,U,E,S, it was measured, respectively, as n 50 = 1.5-0.7-1.8-1.4-2.3 h −1 . We consider an even distribution on the prorata of the external wall surfaces. For the internal  to the adjacent flats accounted for 27% of the total air leakage from the unit. Air leakage between flats in multi-family residential buildings was reported to account for 12%-33% of total air leakage at 50 Pa in a Swedish study. 86 In an experimental study conducted on six flats in four multi-family residential buildings located in Quebec, Canada, the authors measured internal air leakage of 19%-22%-34%-64%-65%-67% of the total air leakage of the six flats. 87 Specifically, they characterized the proportion between adjacent flats and common areas/halls. The latter walls are more airtight, accounting for 11%-n/a-32%-46%-37%-52% of the total air leakage from the flat, respectively. A final study proposes values to be provided to the model for leakage rates at 50 Pa pressure (q 50 ) for each type of wall separating two parts of a multi-family building. These are the data from the study by Lozinsky and Touchie,88 which is based on recent inter-zonal air leakage tests conducted in 12 newly constructed multi-family buildings in Canada. In conclusion, after having analyzed all these data from the literature, the data that we use in our modeling are calculated from the proportions of q 50 proposed by the last study 88

| Three modeled ventilation systems
We study three options for the ventilation systems, selecting reference systems at least in France but also in Western Europe. [67][68][69][70][71] They are whole-house systems complying with the French airing regulation, 89   Note: In bold, the most exposed occupants.  89 Also, we assume that the extracted airflow is switched on twice a day for 1 h to a peak value during cooking periods. The extracted airflows are given in Table 3. As a result, the total exhaust airflow for the reference apartment is 105 m 3 h −1 , accounting for an average dwelling air change rate of 0.5 h −1 , potentially increased to 1 h −1 during cooking periods.
In the BV system, each bedroom is equipped with a supply vent, while the living room has two such vents, sized to balance the total exhaust flow. Supplied airflows are given in Table 4. In

| Door and window openingmodeling and scenarios
This study considers a situation in which different windows are

| Contaminated particlesemission and transfer
There are still many uncertainties about the characterization of the SARS-CoV-2 aerosols, their reactivity on surfaces and the size of the agglomerated particles that may contain the SARS-CoV-2; in any case, these may vary in size depending on the situation. The In our study, as in the calculation tool developed by REHVA, 96 we assume that the infected occupant is at rest throughout the modeling, emitting contaminated particles at a constant rate, which corresponds to the 90 ème percentile of Buonnano 97 : 3.1 quanta h −1 .
We also introduce the decay rate of the virus λ, its value varies be- (4) q out,i = out 4.79 Δ P 0.53 As regards passage through leak points, we need to consider the penetration factor; the higher this factor, the more the particles can penetrate via the leak points. A penetration factor of one means that the leak point presents no obstacle to the passage of the particle.
Liu and Nazaroff 98 measured penetration factors in the laboratory, for different particle sizes (0.02-7 μm) and for cracks with variable geometry (height from 0.25 to 1 mm, length from 4 to 10 cm), on various materials (aluminum, brick, concrete, timber, and plywood), with a pressure reduction of 4 or 10 Pascals. They then compared their measurements with results from the model they developed.
They conclude that for particles with a diameter of 0.1-1.0 μm, with a depression >4 Pascals, this penetration factor is close to 1 (no filtration). They also showed that on an aluminum plate, with a depression of 4 Pascals, the penetration factor is lowered to 0. With these data from the literature and facing many uncertainties about characterization of the SARS-CoV-2 aerosols, we assume a penetration factor of 1. Indeed, once a window is opened, the pressures exerted on the interior walls can reach levels similar to the pressures normally exerted on exterior walls, regularly reaching −2 Pa, and as low as −7 to −11 Pa (strong wind) in our simulations.

| Reference case and studied scenarios
In the reference case, all the internal doors and all the windows of the house are closed. We will also follow the recommendation of the To study the sensitivity of our results, we studied six mitigation scenarios, summarized in Table 5.

| Relative exposure and probability of infection as performance indicators
As a very common indicator by [100][101][102][103][104] and as proposed by, 3 in this study, we firstly examine the cumulative exposure to the contaminated particles Ej, for each occupant j (Equation 7). We calculate it, and we compare it to the reference case exposure, in order to assess the relative performances of different strategies.
where C j (t i ) is the exposure concentration for occupant j at the time step Δ t i = 10 min.Since the infecting dose necessary for SARS-CoV-2 to transmit successfully is still unknown, as for other viruses, our results are valuable only for the purposes of making a relative comparison, and not for their absolute values.
This cumulative exposure is calculated considering the occupancy schedules given in Table 1, over the 2-week simulated period Pease. 105 The probability of infection P is calculated, based on a Poisson distribution, as follows: where μ is the average number of quanta (one quantum gives a 63% probability of inducing infection) breathed in by a person likely to be infected, that is, a person who is exposed to the virus.
To obtain the average number of quanta breathed from the concentration of quanta, we use the method of Rudnich and Milton 105,106 : where C i are the concentrations in quanta per volume, p is the volumetric breathing rate, and t 1 and t 2 are the start and end times of

| RE SULTS AND D ISCUSS I ON
The results include the occupants' exposure for different strategies of windows and doors opening, presented in comparison with the reference case (windows and doors), the probability of infection of the occupants, and the airflows through the walls of the quarantine room. We present in detail the EV case, probably the most common case in the Western European residential building stock. [67][68][69][70][71] Then, we give an overview of the results with the two other ventilation systems.

| Exhaust-only ventilation (EV)
The relative exposures of the seven most exposed occupants of the multi-family building (in the reference flat and in the adjacent flats) compared with the reference case, for a building equipped with EV are given in Table 6. As this type of ventilation system extracts airflows from high-moisture rooms, it creates a pressure difference with respect to the living room and bedrooms, where fresh air enters through grilles placed in the wall or on the windows, thanks to the pressure differences created, plus the wind and stack effects. With this kind of ventilation system, there are higher pressure differences between rooms (than with balanced ones), which causes air to flow from room to room. In this case, we observe that opening the window in the quarantine room always results in increased exposure for at least one other occupant, including in neighbors' dwellings. Some scenarios even cause extremely high relative increases. Indeed, the scenarios can be separated into two groups: the scenarios where the door of the quarantine room is sealed (sc.1,4,5,&6) and the sce- • In the first group of scenarios, the three occupants living in adjacent apartments experience an extreme increase in exposure: +155% (Occ. 6, same floor); +286% (Occ 4, floor above); +2.8 10 5 % (Occ 18, floor below). This last extreme variation reflects a very low absolute value in the reference case. In addition, inside the reference apartment, two occupants exposures increase (+377% and + 574%) and one decrease (−82%).
• The dilution strategies show much better results. Indeed, the exposure rates decrease for four occupants in the high dilution scenario (sc.3), from −16% to −58%, and for 3 occupants in the low dilution scenario (sc.2), from −20% to −61%. The low dilution scenario is the most effective since only one occupant of the reference apartment (Occ. 8) and one neighbor (Occ. 18, below floor) is more exposed, respectively, +8% and +451%. In the high dilution scenario, Occ. 8 and Occ. 18 are also more exposed, respectively, +26% and +683%, also occupant 9 has an increase of 3% which is acceptable, compared with the benefits of the other occupants.
• In this geometry of apartment, opening one or more windows has no impact on occupant exposures. Indeed, scenarios 1, 4, and 5 give equivalent results. Only the scenario of half-opening the windows gives slightly higher increases in exposure.
We are now refining the study with the second indicator, the probability of infection (Table 7). In the reference scenario, all occupants have less than a 1.6% probability of being infected by the virus, it is important that the proposed strategies do not increase this risk. We observe the same two groups of scenarios: • All four scenarios of first group result in much higher risks of infection for all the occupants except Occ. 8, in particular Occ.  • The dilution strategies (sc 2&3) are much more effective as they allow almost all inhabitants to see their risk of infection decrease.

Occupant 8 (reference apartment) is again an exception with a risk
of infection considered as low (<1%).
Finally, the analysis of the inflows and outflows, cumulated over the simulation period, through the different walls of the quarantine room helps to understand these results (Table 8

| Sensitivity of the results to the two other ventilation systems
We calculate also these three indicators: relative exposures, probability of infection, and cumulated airflows through the walls of the quarantine room for the two other ventilation systems: the BV and RH-DCV ones. We observe similar results on the following points: • We observe the same groups of scenarios with different types of impacts.
• In the first group, the three occupants living in adjacent apartments experience high but lower increase in exposure, the lowest being obtained with the RH-DCV: +38% (Occ. 6, same floor); +209% (Occ 4, floor above); +3265% (Occ 18, floor below). The probability of infection of the neighbor Occ. 4 (appt U, above) stays between 4% with BV and 6.4% with RH-DCV. The probability of infection of the neighbor Occ. 6 (appt E, same floor) stays very low whatever the ventilation system (<1%) • With the dilution strategies, the same tendency is observed with decreased exposures, but contrary to EV, all the occupants, including the neighbor Occ. 18 experience these decreases (−31; −94%). All occupants out of the apartments see their risk of infection decrease.
• Opening one or more windows has a very slight impact on occupant exposures and on probability of infection. It confirms that with this geometry of apartment, more the opening of the window, the sealing of the door has a strong negative impact on the occupants' exposure, whatever the ventilation system. Only some differences to the EV system exist on the following points: • For the BV and RH-EV systems, all the scenarios are beneficial for the quarantined occupant (Occ. 11), with exposure decreases between −3 and −42%.
• In the reference cases, the probability of infection is lower with the BV (max. 1.15%), and higher with the RH-DCV (max 2.04%), against 1.65% max with EV.

| Discussion
In the residential building case study, opening the windowsincluding the window of the quarantine room-can decrease or increase the exposure of other occupants, including in neighbors' apartments. It will more depend on the position of the internal door of the quarantine room than on the ventilation system. This is mainly due to air leakage between adjacent rooms at increased flowrates

| CON CLUS I ON AND PER S PEC TIVE S
Ventilation of buildings has been an area of intensive research for some time, due to the energy and health impacts associated with indoor air quality. In a virus pandemic context, ventilation of buildings has also been characterized as a risk in some cases (for instance, air recirculation), but overall offers a solution that could curb or even prevent aerosol transmission of a virus. As ventilation systems are responsible for pressure differences between zones in the same building, any recommendation for window opening and door sealing must take into account the airflows between all zones due to these pressure differences. In our simulations, considering one inhabitant in a quarantine room, we assess the risk of virus transmission for all inhabitants of a multi-family dwellings due to these airflows in various scenarios. We observe that the recommendation to seal the door to the quarantine area, when a mechanical ventilation system is in operation, can strongly increase the probability of infection of several building occupants. These impacts can easily be explained by studying the airflows outgoing and entering the quarantine room, including the different leakages on the external and internal partitions, floors, and ceilings, and how they are impacted by the different strategies.
Nevertheless, as our simulations are for a single multi-family dwelling, with many fixed values for parameters that can have a significant impact on the results, we are conducting further research to better understand the role of ventilation systems regarding airflows between zones.
We have illustrated the importance of moving from a single-zone approach to a multizone approach to quantify the impacts of ventilation and airing in multizone buildings such as residences in order to prevent outbreaks of viruses such as SARS-CoV-2.
Before these results can be used to make general recommendations, they need to be studied in more detail. Firstly, sensitivity analyses need to be carried out for many parameters, such as air leakage TA B L E 8 Cumulated airflows (kg s −1 ) through the different walls of the quarantine room for the 6 studied scenarios, with exhaust-only ventilation (EV)

CO N FLI C T O F I NTE R E S T
No conflicts of interest to declare.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.